Abstract

Meta-analysis is the statistical part of a systematic review. Many researchers haveused selection functions to model publication bias in a meta-analysis. The mainproblem with this approach is that it is impossible to verify that the selection functiontruly represents the selection process, and so the use of selection functions can onlybe seen as part of a sensitivity analysis. In this thesis we present new methods thatinvolve selection functions that aim to make as few strong assumptions about selectionas possible, including the use of a non-parametric permutation test, and the use of astep selection function. We also investigate the use of parametric selection functionsand suggest how researchers could use these as part of a sensitivity analysis, by lookingat a range of plausible values for the overall selection probability. As part of thissensitivity analysis, we assess the effectiveness of the Bounds method as presentedby Henmi et al. Throughout the thesis we illustrate all methods with numericalexamples, including a meta-analysis investigating the effects of environmental tobaccosmoke on the risk of lung cancer in non-smokers.